Sunday, 27 March 2016

Are You Living in a Computer Simulation?

Are You Living in a Computer Simulation?

By Nick Bostrom, Faculty of Philosophy, Oxford University

This paper argues
that at least one of the following propositions is true: (1) the human
species is very likely to go extinct before reaching a “posthuman” stage; (2)
any posthuman civilization is extremely unlikely to run a significant number of
simulations of their evolutionary history (or variations thereof); (3) we are
almost certainly living in a computer simulation.

It follows that the belief
that there is a significant chance that we will one day become posthumans who
run ancestor-simulations is false, unless we are currently living in a
simulation. A number of other consequences of this result are also discussed.

INTRODUCTION

Many
works of science fiction as well as some forecasts by serious technologists and
futurologists predict that enormous amounts of computing power will be
available in the future.
Let us suppose for a moment that these predictions are correct. One thing that
later generations might do with their super-powerful computers is run detailed
simulations of their forebears or of people like their forebears. Because their
computers would be so powerful, they could run a great many such simulations.

Suppose
that these simulated people are conscious (as they would be if the simulations
were sufficiently fine-grained and if a certain quite widely accepted position
in the philosophy of mind is correct). Then it could be the case that the vast
majority of minds like ours do not belong to the original race but rather to
people simulated by the advanced descendants of an original race. It is then
possible to argue that, if this were the case, we would be rational to think
that we are likely among the simulated minds rather than among the original
biological ones. Therefore, if we don’t think that we are currently living in a
computer simulation, we are not entitled to believe that we will have
descendants who will run lots of such simulations of their forebears. That is
the basic idea. The rest of this paper will spell it out more carefully.

Apart form the interest
this thesis may hold for those who are engaged in futuristic speculation, there
are also more purely theoretical rewards. The argument provides a stimulus for
formulating some methodological and metaphysical questions,
and it suggests naturalistic analogies to certain traditional religious
conceptions, which some may find amusing or thought-provoking.

The structure of the paper is as
follows. First, we formulate an assumption that we need to import from the
philosophy of mind in order to get the argument started. Second, we consider
some empirical reasons for thinking that running vastly many simulations of
human minds would be within the capability of a future civilization that has
developed many of those technologies that can already be shown to be compatible
with known physical laws and engineering constraints. This part is not
philosophically necessary but it provides an incentive for paying attention to
the rest. Then follows the core of the argument, which makes
use of some simple probability theory, and a section providing support for a
weak indifference principle that the argument employs. Lastly, we
discuss some interpretations of the disjunction, mentioned in the abstract, that forms the conclusion of the simulation
argument.

THE ASSUMPTION OF
SUBSTRATE-INDEPENDENCE

A
common assumption in the philosophy of mind is that of substrate-independence. The idea is that
mental states can supervene on any of a broad class of physical substrates.
Provided a system implements the right sort of computational structures and
processes, it can be associated with conscious experiences. It is not an
essential property of consciousness that it is implemented on carbon-based
biological neural networks inside a cranium: silicon-based processors inside a
computer could in principle do the trick as well.

Arguments for this thesis have been given in
the literature, and although it is not entirely uncontroversial, we shall here
take it as a given.

The argument we shall present does not,
however, depend on any very strong version of functionalism or
computationalism. For example, we need not assume that the thesis of substrate-independence
is necessarily true (either analytically or metaphysically) – just that,
in fact, a computer running a suitable program would be conscious. Moreover, we
need not assume that in order to create a mind on a computer it would be
sufficient to program it in such a way that it behaves like a human in all
situations, including passing the Turing test etc. We need only the weaker
assumption that it would suffice for the generation of subjective experiences
that the computational processes of a human brain are structurally replicated
in suitably fine-grained detail, such as on the level of individual synapses.
This attenuated version of substrate-independence is quite widely accepted.

Neurotransmitters, nerve growth factors, and
other chemicals that are smaller than a synapse clearly play a role in human
cognition and learning. The substrate-independence thesis is not that the
effects of these chemicals are small or irrelevant, but rather that they affect
subjective experience only via their direct or indirect influence on
computational activities. For example, if there can be no difference in
subjective experience without there also being a difference in synaptic
discharges, then the requisite detail of simulation is at the synaptic level
(or higher).

THE TECHNOLOGICAL
LIMITS OF COMPUTATION

At
our current stage of technological development, we have neither sufficiently
powerful hardware nor the requisite software to create conscious minds in
computers. But persuasive arguments have been given to the effect that if
technological progress continues unabated then these shortcomings will
eventually be overcome. Some authors argue that this stage may be only a few
decades away.[1][1] Yet present purposes
require no assumptions about the time-scale. The simulation argument works
equally well for those who think that it will take hundreds of thousands of
years to reach a “posthuman” stage of civilization, where humankind has
acquired most of the technological capabilities that one can currently show to
be consistent with physical laws and with material and energy constraints.

Such a mature stage of technological
development will make it possible to convert planets and other astronomical
resources into enormously powerful computers. It is currently hard to be
confident in any upper bound on the computing power that may be available to
posthuman civilizations. As we are still lacking a “theory of everything”, we
cannot rule out the possibility that novel physical phenomena, not allowed for
in current physical theories, may be utilized to transcend those constraints[2][2] that in our current
understanding impose theoretical limits on the information processing
attainable in a given lump of matter. We can with much greater confidence
establish lower bounds on posthuman computation, by assuming only
mechanisms that are already understood. For example, Eric Drexler has outlined
a design for a system the size of a sugar cube (excluding cooling and power
supply) that would perform 1021 instructions per second.[3][3] Another author gives
a rough estimate of 1042 operations per second for a computer with a
mass on order of a large planet.[4][4] (If we could create
quantum computers, or learn to build computers out of nuclear matter or plasma,
we could push closer to the theoretical limits. Seth Lloyd calculates an upper
bound for a 1 kg computer of 5*1050 logical operations per second
carried out on ~1031 bits.[5][5] However, it suffices
for our purposes to use the more conservative estimate that presupposes only
currently known design-principles.)

The amount of computing power needed to
emulate a human mind can likewise be roughly estimated. One estimate, based on
how computationally expensive it is to replicate the functionality of a piece
of nervous tissue that we have already understood and whose functionality has
been replicated in silico, contrast
enhancement in the retina, yields a figure of ~1014 operations per
second for the entire human brain.[6][6] An alternative
estimate, based the number of synapses in the brain and their firing frequency,
gives a figure of ~1016-1017 operations per second.[7][7] Conceivably, even
more could be required if we want to simulate in detail the internal workings
of synapses and dendritic trees. However, it is likely that the human central
nervous system has a high degree of redundancy on the mircoscale
to compensate for the unreliability and noisiness of its neuronal components.
One would therefore expect a substantial efficiency gain when using more
reliable and versatile non-biological processors.

Memory seems to be a no more stringent
constraint than processing power.[8][8] Moreover, since the
maximum human sensory bandwidth is ~108 bits per second, simulating
all sensory events incurs a negligible cost compared to simulating the cortical
activity. We can therefore use the processing power required to simulate the
central nervous system as an estimate of the total computational cost of
simulating a human mind.

If the environment is included in the
simulation, this will require additional computing power – how much depends on
the scope and granularity of the simulation. Simulating the entire universe
down to the quantum level is obviously infeasible, unless radically new physics
is discovered. But in order to get a realistic simulation of human experience,
much less is needed – only whatever is required to ensure that the simulated
humans, interacting in normal human ways with their simulated environment,
don’t notice any irregularities.

The microscopic structure of the inside of
the Earth can be safely omitted. Distant astronomical objects can have highly
compressed representations: verisimilitude need extend to the narrow band of
properties that we can observe from our planet or solar system spacecraft. On
the surface of Earth, macroscopic objects in inhabited areas may need to be
continuously simulated, but microscopic phenomena could likely be filled in ad
hoc. What you see through an electron microscope needs to look
unsuspicious, but you usually have no way of confirming its coherence with
unobserved parts of the microscopic world. Exceptions arise when we
deliberately design systems to harness unobserved microscopic phenomena that
operate in accordance with known principles to get results that we are able to
independently verify. The paradigmatic case of this is a computer. The
simulation may therefore need to include a continuous representation of
computers down to the level of individual logic elements. This presents no
problem, since our current computing power is negligible by posthuman standards.

Moreover, a posthuman simulator would have
enough computing power to keep track of the detailed belief-states in all human
brains at all times. Therefore, when it saw that a human was about to make an
observation of the microscopic world, it could fill in sufficient detail in the
simulation in the appropriate domain on an as-needed basis. Should any error
occur, the director could easily edit the states of any brains that have become
aware of an anomaly before it spoils the simulation.
Alternatively, the director could skip back a few seconds and rerun the
simulation in a way that avoids the problem.

It thus seems plausible that the main
computational cost in creating simulations that are indistinguishable from
physical reality for human minds in the simulation resides in simulating
organic brains down to the neuronal or sub-neuronal level.[9][9] While it is not
possible to get a very exact estimate of the cost of a realistic simulation of
human history, we can use ~1033 - 1036 operations as a
rough estimate[10][10]. As we gain more
experience with virtual reality, we will get a better grasp of the
computational requirements for making such worlds appear realistic to their
visitors. But in any case, even if our estimate is off by several orders of
magnitude, this does not matter much for our argument. We noted that a rough
approximation of the computational power of a planetary-mass computer is 1042
operations per second, and that assumes only already known
nanotechnological designs, which are probably far from optimal. A single such a
computer could simulate the entire mental history of humankind (call this an ancestor-simulation)
by using less than one millionth of its processing power for one second. A
posthuman civilization may eventually build an astronomical number of such
computers. We can conclude that the computing power available to a posthuman
civilization is sufficient to run a huge number of ancestor-simulations even it
allocates only a minute fraction of its resources to that purpose. We can draw
this conclusion even while leaving a substantial margin of error in all our
estimates.

·
Posthuman
civilizations would have enough computing power to run hugely many
ancestor-simulations even while using only a tiny fraction of their resources
for that purpose.

THE
CORE OF THE SIMULATION ARGUMENT

The
basic idea of this paper can be expressed roughly as follows: If there were a substantial chance that our civilization will ever
get to the posthuman stage and run many ancestor-simulations, then how come you
are not living in such a simulation?

We shall develop this idea into a
rigorous argument. Let us introduce the following notation:

: Fraction of all
human-level technological civilizations that survive to reach a posthuman stage

: Average number of
ancestor-simulations run by a posthuman civilization

: Average number of
individuals that have lived in a civilization before it reaches a posthuman
stage

The
actual fraction of all observers with human-type experiences that live in
simulations is then

Writing for the fraction of posthuman civilizations
that are interested in running ancestor-simulations (or that contain at least
some individuals who are interested in that and have sufficient resources to
run a significant number of such simulations), and for the average number of ancestor-simulations
run by such interested civilizations, we have

and thus:

(*)

Because
of the immense computing power of posthuman civilizations, is extremely large, as we saw in the previous
section. By inspecting (*) we can then see that at least one of the
following three propositions must be true:

(1)

(2)

(3)

A BLAND INDIFFERENCE
PRINCIPLE

We
can take a further step and conclude that conditional on the truth of (3),
one’s credence in the hypothesis that one is in a simulation should be close
to unity. More generally, if we knew that a fraction x of all observers
with human-type experiences live in simulations, and we don’t have any
information that indicate that our own particular experiences are any more or
less likely than other human-type experiences to have been implemented in
vivo rather than in machina, then our
credence that we are in a simulation should equal x:

(#)

This
step is sanctioned by a very weak indifference principle. Let us distinguish
two cases. The first case, which is the easiest, is where all the minds in
question are like your own in the sense that they are exactly qualitatively
identical to yours: they have exactly the same information and the same
experiences that you have. The second case is where the minds are “like” each
other only in the loose sense of being the sort of minds that are typical of
human creatures, but they are qualitatively distinct from one another and each
has a distinct set of experiences. I maintain that even in the latter case,
where the minds are qualitatively different, the simulation argument still
works, provided that you have no information that bears on the question of
which of the various minds are simulated and which are implemented biologically.

A detailed defense of a stronger
principle, which implies the above stance for both cases as trivial special
instances, has been given in the literature.[11][11]Space does not permit
a recapitulation of that defense here, but we can bring out one of the
underlying intuitions by bringing to our attention to an analogous situation of
a more familiar kind. Suppose that x% of the population has a certain
genetic sequence S within the part of their DNA commonly designated as
“junk DNA”. Suppose, further, that there are no manifestations of S
(short of what would turn up in a gene assay) and that there are no known
correlations between having S and any observable characteristic. Then,
quite clearly, unless you have had your DNA sequenced, it is rational to assign
a credence of x% to the hypothesis that you
have S. And this is so quite irrespective of the fact that the people
who have S have qualitatively different minds and experiences from the
people who don’t have S. (They are different simply because all humans
have different experiences from one another, not because of any known link
between S and what kind of experiences one has.)

The same reasoning holds if S is not the
property of having a certain genetic sequence but instead the property of being
in a simulation, assuming only that we have no information that enables us to
predict any differences between the experiences of simulated minds and those of
the original biological minds.

It should be stressed that the bland
indifference principle expressed by (#) prescribes indifference only between
hypotheses about which observer you are, when you have no information about
which of these observers you are. It does not in general prescribe indifference
between hypotheses when you lack specific information about which of the
hypotheses is true. In contrast to Laplacean and
other more ambitious principles of indifference, it is therefore immune to
Bertrand’s paradox and similar predicaments that tend to plague indifference
principles of unrestricted scope.

Readers familiar with the Doomsday argument[12][12] may worry that the
bland principle of indifference invoked here is the same assumption that is
responsible for getting the Doomsday argument off the ground, and that the
counterintuitiveness of some of the implications of the latter incriminates or
casts doubt on the validity of the former. This is not so. The Doomsday
argument rests on a much stronger and more controversial premiss, namely
that one should reason as if one were a random sample from the set of all
people who will ever have lived (past, present, and future) even though we
know that we are living in the early twenty-first century rather than at
some point in the distant past or the future. The bland indifference principle,
by contrast, applies only to cases where we have no information about which
group of people we belong to.

If betting odds provide some guidance to
rational belief, it may also be worth to ponder that if everybody were to place
a bet on whether they are in a simulation or not, then if people use the bland
principle of indifference, and consequently place their money on being in a
simulation if they know that that’s where almost all people are, then almost
everyone will win their bets. If they bet on not being in a simulation,
then almost everyone will lose. It seems better that the bland indifference
principle be heeded.

Further, one can consider a sequence of
possible situations in which an increasing fraction of all people live in
simulations: 98%, 99%, 99.9%, 99.9999%, and so on. As one approaches the
limiting case in which everybody is in a simulation (from which one can deductively
infer that one is in a simulation oneself), it is plausible to require that the
credence one assigns to being in a simulation gradually approach the limiting
case of complete certainty in a matching manner.

INTERPRETATION

The
possibility represented by proposition (1) is fairly straightforward. If (1) is true,
then humankind will almost certainly fail to reach a posthuman level; for
virtually no species at our level of development become posthuman, and it is
hard to see any justification for thinking that our own species will be
especially privileged or protected from future disasters. Conditional on (1),
therefore, we must give a high credence to DOOM, the hypothesis that
humankind will go extinct before reaching a posthuman level:

One can imagine hypothetical situations were
we have such evidence as would trump knowledge of . For example,
if we discovered that we were about to be hit by a giant meteor, this might
suggest that we had been exceptionally unlucky. We could then assign a credence to DOOM larger than our expectation of the
fraction of human-level civilizations that fail to reach posthumanity. In the
actual case, however, we seem to lack evidence for thinking that we are special
in this regard, for better or worse.

Proposition (1) doesn’t by itself
imply that we are likely to go extinct soon, only that we are unlikely to reach
a posthuman stage. This possibility is compatible with us remaining at, or somewhat
above, our current level of technological development for a long time before
going extinct. Another way for (1) to be true is if it is likely that
technological civilization will collapse. Primitive human societies might then
remain on Earth indefinitely.

There are many ways in which humanity could
become extinct before reaching posthumanity. Perhaps the most natural
interpretation of (1) is that we are likely to go extinct as a result of the
development of some powerful but dangerous technology.[13][13] One candidate is
molecular nanotechnology, which in its mature stage would enable the
construction of self-replicating nanobots capable of feeding on dirt and
organic matter – a kind of mechanical bacteria. Such nanobots, designed for
malicious ends, could cause the extinction of all life on our planet.[14][14]

The second alternative in the
simulation argument’s conclusion is that the fraction of posthuman
civilizations that are interested in running ancestor-simulation is negligibly
small. In order for (2) to be true, there must be a strong convergence
among the courses of advanced civilizations. If the number of
ancestor-simulations created by the interested civilizations is extremely
large, the rarity of such civilizations must be correspondingly extreme.
Virtually no posthuman civilizations decide to use their resources to run large
numbers of ancestor-simulations. Furthermore, virtually all posthuman
civilizations lack individuals who have sufficient resources and interest to
run ancestor-simulations; or else they have reliably enforced laws that prevent
such individuals from acting on their desires.

What force could bring about such
convergence? One can speculate that advanced civilizations all develop along a
trajectory that leads to the recognition of an ethical prohibition against
running ancestor-simulations because of the suffering that is inflicted on the
inhabitants of the simulation. However, from our present point of view, it is
not clear that creating a human race is immoral. On the contrary, we tend to
view the existence of our race as constituting a great ethical value. Moreover,
convergence on an ethical view of the immorality of running
ancestor-simulations is not enough: it must be combined with convergence on a
civilization-wide social structure that enables activities considered immoral
to be effectively banned.

Another possible convergence point is
that almost all individual posthumans in virtually all posthuman civilizations
develop in a direction where they lose their desires to run ancestor-simulations.
This would require significant changes to the motivations driving their human
predecessors, for there are certainly many humans who would like to run
ancestor-simulations if they could afford to do so. But perhaps many of our
human desires will be regarded as silly by anyone who becomes a posthuman.
Maybe the scientific value of ancestor-simulations to a posthuman civilization
is negligible (which is not too implausible given its unfathomable intellectual
superiority), and maybe posthumans regard recreational activities as merely a
very inefficient way of getting pleasure – which can be obtained much more
cheaply by direct stimulation of the brain’s reward centers. One conclusion
that follows from (2) is that posthuman societies will be very different from
human societies: they will not contain relatively wealthy independent agents
who have the full gamut of human-like desires and are free to act on them.

The possibility expressed by
alternative (3) is the conceptually most intriguing one. If we are living in a
simulation, then the cosmos that we are observing is just a tiny piece of the
totality of physical existence. The physics in the universe where the computer
is situated that is running the simulation may or may not resemble the physics
of the world that we observe. While the world we see is in some sense “real”,
it is not located at the fundamental level of reality.

It may be possible for simulated
civilizations to become posthuman. They may then run their own
ancestor-simulations on powerful computers they build in their simulated
universe. Such computers would be “virtual machines”, a familiar concept in
computer science. (Java script web-applets, for instance, run on a virtual
machine – a simulated computer – inside your desktop.) Virtual machines can be
stacked: it’s possible to simulate a machine simulating another machine, and so
on, in arbitrarily many steps of iteration. If we do go on to create our own
ancestor-simulations, this would be strong evidence against (1) and (2), and we
would therefore have to conclude that we live in a simulation. Moreover, we
would have to suspect that the posthumans running our simulation are themselves
simulated beings; and their creators, in turn, may also be simulated beings.

Reality may thus contain many levels.
Even if it is necessary for the hierarchy to bottom out at some stage – the
metaphysical status of this claim is somewhat obscure – there may be room for a
large number of levels of reality, and the number could be increasing over time.
(One consideration that counts against the multi-level hypothesis is that the
computational cost for the basement-level simulators would be very great.
Simulating even a single posthuman civilization might be prohibitively
expensive. If so, then we should expect our simulation to be terminated when we
are about to become posthuman.)

Although all the elements of such a
system can be naturalistic, even physical, it is possible to draw some loose
analogies with religious conceptions of the world. In some ways, the posthumans
running a simulation are like gods in relation to the people inhabiting the
simulation: the posthumans created the world we see; they are of superior
intelligence; they are “omnipotent” in the sense that they can interfere in the
workings of our world even in ways that violate its physical laws; and they are
“omniscient” in the sense that they can monitor everything that happens.
However, all the demigods except those at the fundamental level of reality are
subject to sanctions by the more powerful gods living at lower levels.

Further rumination on these themes could
climax in a naturalistic theogony that would
study the structure of this hierarchy, and the constraints imposed on its
inhabitants by the possibility that their actions on their own level may affect
the treatment they receive from dwellers of deeper levels. For example, if
nobody can be sure that they are at the basement-level, then everybody would
have to consider the possibility that their actions will be rewarded or punished,
based perhaps on moral criteria, by their simulators. An afterlife would be a
real possibility. Because of this fundamental uncertainty, even the basement
civilization may have a reason to behave ethically. The fact that it has such a
reason for moral behavior would of course add to everybody else’s reason for
behaving morally, and so on, in truly virtuous circle. One might get a kind of
universal ethical imperative, which it would be in everybody’s self-interest to
obey, as it were “from nowhere”.

In addition to ancestor-simulations, one may
also consider the possibility of more selective simulations that include only a
small group of humans or a single individual. The rest of humanity would then
be zombies or “shadow-people” – humans simulated only at a level sufficient for
the fully simulated people not to notice anything suspicious. It is not clear
how much cheaper shadow-people would be to simulate than real people. It is not
even obvious that it is possible for an entity to behave indistinguishably from
a real human and yet lack conscious experience. Even if there are such
selective simulations, you should not think that you are in one of them unless
you think they are much more numerous than complete simulations. There would
have to be about 100 billion times as many “me-simulations” (simulations of the
life of only a single mind) as there are ancestor-simulations in order for most
simulated persons to be in me-simulations.

There is also the possibility of simulators
abridging certain parts of the mental lives of simulated beings and giving them
false memories of the sort of experiences that they would typically have had
during the omitted interval. If so, one can consider the following (farfetched)
solution to the problem of evil: that there is no suffering in the world and
all memories of suffering are illusions. Of course, this hypothesis can be
seriously entertained only at those times when you are not currently suffering.

Supposing we live in a simulation,
what are the implications for us humans? The foregoing remarks notwithstanding,
the implications are not all that radical. Our best guide to how our posthuman
creators have chosen to set up our world is the standard empirical study of the
universe we see. The revisions to most parts of our belief networks would be
rather slight and subtle – in proportion to our lack of confidence in our
ability to understand the ways of posthumans. Properly understood, therefore,
the truth of (3) should have no tendency to make us “go crazy” or to prevent us
from going about our business and making plans and predictions for tomorrow.
The chief empirical importance of (3) at the current time seems to lie in its
role in the tripartite conclusion established above.[15][15]We may hope that (3)
is true since that would decrease the probability of (1), although if
computational constraints make it likely that simulators would terminate a
simulation before it reaches a posthuman level, then out best hope would be
that (2) is true.

If we learn more about posthuman motivations
and resource constraints, maybe as a result of developing towards becoming
posthumans ourselves, then the hypothesis that we are simulated will come to
have a much richer set of empirical implications.

CONCLUSION

A
technologically mature “posthuman” civilization would have enormous computing
power.
Based on this empirical fact, the simulation argument shows that at least
one of the following propositions is true: (1) The fraction of human-level
civilizations that reach a posthuman stage is very close to zero; (2) The
fraction of posthuman civilizations that are interested in running
ancestor-simulations is very close to zero; (3) The fraction of all people with
our kind of experiences that are living in a simulation is very close to one.

If (1) is true, then we will almost certainly
go extinct before reaching posthumanity. If (2) is true, then there must be a
strong convergence among the courses of advanced civilizations so that
virtually none contains any relatively wealthy individuals who desire to run
ancestor-simulations and are free to do so. If (3) is true, then we almost
certainly live in a simulation. In the dark forest of
our current ignorance, it seems sensible to apportion one’s credence roughly
evenly between (1), (2), and (3).

Unless
we are now living in a simulation, our descendants will almost certainly never
run an ancestor-simulation.

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[15][15] For some reflections by another
author on the consequences of (3), which were sparked by a privately circulated
earlier version of this paper, see R. Hanson, “How to Live in a Simulation.” Journal of Evolution and
Technology, vol. 7 (2001).

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